Feedforward nonlinear equalization of modulated data signals

• US 4,213,095 A
• Filed: 08/04/1978
• Issued: 07/15/1980
• Est. Priority Date: 08/04/1978
• Status: Expired due to Term

• Current Assignee: Bell Telephone Laboratories, Inc. (Nokia Corporation)
• Original Assignee: Bell Telephone Laboratories, Inc. (Nokia Corporation)
• Inventors: Falconer, David D.
• Primary Examiner(s): Safourek, Benedict V.
• Application Number:
  US05/931,026
• Time in Patent Office: 711 Days
• Field of Search: 325/41, 325/42, 325/65, 325/320, 325/321, 325/323, 325/473, 328/155, 328/162, 333/17, 333/18, 340/347 DD
• US Class Current: 375/232
• CPC Class Codes: H04L 27/01 Equalisers baseband equalizers at the transmitter end H04L25/03343; in analogue transmission systems H04B3/04, H04B7/005

Abstract

A feedforward nonlinear signal (P(n)) is added to each sample of a linearly equalized received signal (Q(n)) to provide compensation for nonlinear intersymbol interference. The received signal is a modulated data signal impaired by linear and nonlinear distortion as well as phase jitter and additive noise. The feedforward nonlinear signal added to each sample is comprised of a weighted sum of products of individual ones of the samples and their complex conjugates. Each multiplicand bears a predetermined temporal relationship to the sample currently being processed. In an illustrative embodiment, compensation for second- and third-order intersymbol interference is provided by including two- and three-multiplicand weighted products in the feedforward nonlinear signal. Weighting coefficients for each product are adaptively updated in a decision-directed manner.

Claims

1. In an arrangement responsive to samples of a received modulated data signal for forming decisions as to the values of data symbols contained in said signal, each of said samples being represented by a complex number, that improvement which comprises

means (51-55, 61-65) for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71-75) for multiplying each of said products by an associated coefficient to form a plurality of weighted products,

means (81-86) for combining said weighted products with each other to generate a feedforward nonlinear signal, and

means (12, 14, 17, 43) for forming an individual one of said decisions in response to said feedforward nonlinear signal.

2. The invention of claim 1 wherein said modulated data signal is of the type in which both the carrier phase and amplitude are information-bearing.

3. The invention of claim 1 wherein said modulated data signal is a quadrature amplitude modulated signal.

4. In an arrangement responsive to samples of a received modulated data signal for forming decisions as to thee values of data symbols contained in said signal, said signal being of the type in which both the carrier phase and amplitude are information bearing and each of said samples being represented by a complex number, that improvement which comprises

means (51-55, 61-65) for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71-75 for multiplying each of said products by an associated coefficient to form a plurality of weighted products,

means (11, 43) for multiplying predetermined ones of said samples by respective associateed coefficients and for summing the resulting products with said weighted products to form a composite feedforward signal and

means (12, 14, 17) responsive to said composite feedforward signal for forming an individual one of said decisions.

5. In an arrangement responsive to complex samples of a received modulated data signal for forming decisions as to the values of data symbols represented by said signal, both the carrier phase and amplitude of said signal being information-bearing, that improvement which comprises

means (51-55, 61-65) operative during each of a plurality of successive sampling periods for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71--75) operative during each of said sampling periods for multiplying said products by respective associated coefficients to form a plurality of weighted products, the value of each of said coefficients during an individual one of said sampling periods being its value during a preceding sampling period modified by a correction factor,

means (81-86) for combining said weighted products with each other to generate a feedforward nonlinear signal,

means (11, 43) responsive to predetermined ones of said samples for generating a feedforward linear signal and for combining it with said feedforward nonlinear signal to form a composite feedforward signal, and

means (12, 14, 17) for forming an individual one of said decisions in response to said composite feedforward signal.

6. The invention of claim 5 further comprising means means (12) for demodulating said composite feedforward signal, means (17) for generating a quantized data signal in response to the demodulated composite feedforward signal, means for forming an error signal (20) in response to said demodulated signal and said quantized data signal, and means (28) for modulating said error signal at the carrier frequency of said modulated data signal to form a modulated error signal, said correction factor for an individual one of said coefficients being a function of the product associated with said individual one of said coefficients during said preceding sampling period and of the modulated error signal for said preceding sampling period.

7. In a method for forming decisions as to the values of data symbols contained in a received modulated data signal, said decisions being formed in response to complex samples of said received signal, that improvement which comprises the steps of

forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying each of said products by an associated coefficient to form a plurality of weighted products,

combining said weighted products with each other to generate a feedforward nonlinear signal, and

forming an individual one of said decisions in response to said feedforward nonlinear signal.

8. The invention of claim 7 wherein said modulated data signal is of the type in which both the carrier phase and amplitude are modulated.

9. The invention of claim 7 wherein said modulated data signal is a quadrature amplitude modulated signal.

10. In a method for forming decisions as to the values of data symbols contained in a received quadrature amplitude modulated data signal, said decisions being formed in response to complex samples of said received signal, that improvement which comprises the steps of

forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying each of said products by an associated coefficient to form a plurality of weighted products,

combining said weighted products with each other to generate a feedforward nonlinear signal,

generating a feedforward linear signal in response to predetermined ones of said samples

combining said feedforward linear signal with said feedforward nonlinear signal to form a composite feedforward signal,

and forming an individual one of said decisions in response to said composite feedforward signal.

11. In a method for forming decisions as to the values of data symbols represented by a received modulated data signal in which both the carrier phase and amplitude are information-bearing, said decisions being formed in response to samples of said received signal each of which is represented by a complex number, that improvement which comprises the steps of

forming during each of a plurality of successive sampling periods a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying said products by respective associated coefficients during each of said sampling periods to form a plurality of weighted products, the value of each of said coefficients during an individual one of said sampling periods being its value during the preceding sampling period modified by a correction factor,

combining said weighted products with each other to generate a feedforward nonlinear signal, and

forming an individual one of said decisions in response to a composite signal which includes said feedforward nonlinear signal.

12. The invention of claim 11 comprising the further steps of multiplying predetermined ones of said samples by respective associated coefficients and combining the resulting products with said feedforward nonlinear signal to form a composite feedforward signal, demodulating said composite feedforward signal, generating a quantized data signal in response to the demodulated composite feedforward signal, forming an error signal in response to said demodulated signal and said quantized data signal, and modulating said error signal at the carrier frequency of said modulated data signal to form a modulated error signal, said correction factor for an individual one of said coefficients being a function of the product associated with said individual one of said coefficients during said preceding sampling period and of the modulated error signal for said preceding sampling period.

13. In an arrangement for receiving a succession of complex samples of a modulated data signal of the type in which both the carrier amplitude and phase are information-bearing, the n^th of said samples being R(n), said signal representing a plurality of data symbols, the method which comprises the steps of

generating an equalized feedforward nonlinear signal P(n) corresponding to said sample R(n), said signal P(n) including the terms ##EQU7## * indicating complex conjugate, the coefficients W_j.sbsb.1.sub.,j.sbsb.2.sup.(1)* (n) and W_j.sbsb.3.sub.,j.sbsb.4.sup.(2)* (n) having respective values associated with said sample R(n), and the index pairs (j₁,j₂) and (j₃,j₄) having respective sets of predetermined values, and

forming a decision A(n) as to the value of an individual one of said data symbols in response to said signal P(n).

14. The invention of claim 13 wherein said decision-generating step is comprised of the steps of forming a demodulated signal Y(n) in response to at least said signal P(n) and quantizing said signal Y(n) to generate said decision A(n),

and wherein said method is comprised of the further steps of forming a modulated error signal J^* (n) in response to said signal Y(n) and said decision A(n), and updating the coefficients W_j.sbsb.1.sub.,j.sbsb.2.sup.(1)* (n) and W_j.sbsb.3.sub.,j.sbsb.4.sup.(2)* (n) in accordance with ##EQU8## β

.sub. (n) and β

₂ (n) being selected scaling factors.

15. The invention of claim 14 comprising the further steps of

generating an equalized feedforward linear signal Q(n), ##EQU9## the coefficients W_i.sup.(0)* (n) having respective values associated with said sample R(n) and the index i having a set of predetermined values, said signal Y(n) being formed also in response to said signal Q(n), and

updating the coefficients W_i.sup.(0)* (n) in accordance with

16. The invention of claim 13 wherein said signal P(n) further includes at least a selected one of the terms ##EQU10## the coefficients W_k.sbsb.1.sub.,k.sbsb.2.sub.,k.sbsb.3.sup.(3)* (n), W_k.sbsb.4.sub.,k.sbsb.5.sub.,k.sbsb.6.sup.(4)* (n) and W_k.sbsb.7.sub.,k.sbsb.8.sub.,k.sbsb.9.sup.(5)* (n) having respective values associated with said sample R(n), and the index triples (k₁,k₂,k₃), (k₄,k₅,k₆) and (k₇,k₈,k₉) having respective sets of predetermined values.

17. The invention of claim 16 wherein said decision-generating step is comprised of the steps of forming a demodulated signal Y(n) in response to at least said signal P(n) and quantizing said signal Y(n) to generate said decision A(n),

and wherein said method is comprised of the further steps of forming a modulated error signal J^* (n) in response to said signal Y(n) and said decision A(n), and updating the coefficients W_k.sbsb.1.sub.,k.sbsb.2.sub.,k.sbsb.3.sup.(3)* (n), W_k.sbsb.4.sub.,k.sbsb.5.sub.,k.sbsb.6.sup.(4)* (n) and W_k.sbsb.7.sub.,k.sbsb.8.sub.,k.sbsb.9.sup.(5)* (n) in accordance with ##EQU11## β

.sub. (n), β

₄ (n) and β

₅ (n) being selected scaling factors.

18. In an arrangement for equalizing samples of a received modulated data signal, said modulated data signal being of the type in which both the carrier phase and amplitude are information-bearing, and each of said samples being represented by a complex number, that improvement which comprises

means (51-55, 61-65) for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71-75) for multiplying each of said products by an associated coefficient to form a plurality of weighted products, and

means (81-86) for combining said weighted products with each other to generate a feedforward nonlinear signal.

20. The invention of claim 18 or claim 19 further comprising means (11, 43) responsive to predetermined ones of said samples for generating a feedforward linear signal and for combining it with said feedforward nonlinear signal to form a composite feedforward signal and means (12, 14, 17) responsive to said composite feedforward signal for recovering the modulated data from said samples.

19. In an arrangement for equalizing samples of a received quadrature amplitude modulated data signal, each of said samples being represented by a complex number, that improvement which comprises

means (51-55, 61-65) for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71-75) for multiplying each of said products by an associated coefficient to form a plurality of weighted products, and

means (81-86) for combining said weighted products with each other to generate a feedforward nonlinear signal.

21. In an arrangement for equalizing complex samples of a received modulated data signal in which both the carrier phase and amplitude are information-bearing, that improvement which comprises

means (51-55, 61-65) operative during each of a plurality of successive sampling periods for forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, at at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

means (71-75) operative during each of said sampling periods for multiplying said products by respective associated coefficients to form a plurality of weighted products, the value of each of said coefficients during an individual one of said sampling being its value during a preceding sampling period modified by a correction factor,

means (81-86) for combining said weighted products with each other to generate a feedforward nonlinear signal,

means (11, 43) responsive to predetermined ones of said samples for generating a feedforward linear signal and for combining it with said feedforward nonlinear signal to form a composite feedforward signal,

means (12) for demodulating said composite feedforward signal,

means (17) for generating a quantized data signal in response to the demodulated composite feedforward signal,

means for forming an error signal (20) in response to said demodulated signal and said quantized data signal, and

means (28) for modulating said error signal at the carrier frequency of said modulated data signal to form a modulated error signal, said correction factor for an individual one of said coefficients being a function of the product associated with said individual one of said coefficients during said preceding sampling period and of the modulated error signal for said preceding sampling period.

22. In a method for equalizing complex samples of a received modulated data signal, said modulated data signal being of the type in which both the carrier phase and amplitude are modulated, that improvement which comprises the steps of

forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying each of said products by an associated coefficient to form a plurality of weighted products, and

combining said weighted products with each other to generate a feedforward nonlinear signal.

24. The invention of claim 22 or claim 23 comprising the further steps of generating a feedforward linear signal in response to predetermined ones of said samples and combining said feedforward linear signal with said feedforward nonlinear signal to form a composite feedforward signal, and recovering the modulated data from said samples in response to said composite feedforward signal.

23. In a method for equalizing complex samples of a received quadrature amplitude modulated data signal, that improvement which comprises the steps of

forming a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying each of said products by an associated coefficient to form a plurality of weighted products, and

combining said weighted products with each other to generate a feedforward nonlinear signal.

25. In a method for equalizing samples of a received modulated data signal in which both the carrier phase and amplitude are information-bearing, each of said samples being represented by a complex number, that improvement which comprises the steps of

forming during each of a plurality of successive sampling periods a plurality of signal products associated with an individual one of said samples, each multiplicand of each product being derived from a respective one of said samples, each said respective one of said samples bearing a predetermined temporal relationship to said individual one of said samples, and at least one multiplicand of individual ones of said signal products being the complex conjugate of the sample from which said one multiplicand is derived,

multiplying said products by respective associated coefficients during each of said sampling periods to form a plurality of weighted products, the value of each of said coefficients during an individual one of said sampling periods being its value during the preceding sampling period modified by a correction factor,

combining said weighted products with each other to generate a feedforward nonlinear signal,

generating a feedforward linear signal in response to predetermined ones of said samples and combining said feedforward linear signal with said feedforward nonlinear signal to form a composite feedforward signal,

demodulating said composite feedforward signal,

generating a quantized data signal in response to the demodulated composite feedforward signal,

forming an error signal in response to said demodulated signal and said quantized data signal, and,

modulating said error signal at the carrier frequency of said modulated data signal to form a modulated error signal, said correction factor for an individual one of said coefficients being a function of the product associated with said individual one of said coefficients during said preceding sampling period and of the modulated error signal for said preceding sampling period.